Nonlinear Interval Optimization of Asymmetric Damper Parameters for a Racing Car

2021 ◽  
pp. 2150013
Author(s):  
Tian Chai ◽  
Xu Han ◽  
Jie Liu ◽  
Bing Zhou ◽  
Fei Lei ◽  
...  
Keyword(s):  
Taylor Series Expansion ◽  
Optimization Method ◽  
Dynamic Responses ◽  
Approximation Model ◽  
Nonlinear Dynamic Response ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Fluctuation Range ◽  
Performance Evaluation Index

Uncertainties in parameters can affect racing car performance. In this study, a nonlinear interval suspension damping optimization method is proposed to improve the road holding of a racing car. To evaluate the dynamic responses of racing cars under a random road input and a bump input with interval uncertain parameters, a quarter car model with a two-stage asymmetric damper is established. Then, a quadratic approximation model with second derivative terms is developed by second-order Taylor series expansion and dimension reduction to calculate the nonlinear dynamic response of the vehicle. Interval analysis of the objective function and constraints is carried out using interval arithmetic to eliminate nesting optimization and make the optimization efficient. The results show that the proposed optimization method can improve road holding performance, effectively suppress the fluctuation range of the road holding performance evaluation index, and ensure the robustness of the design scheme.

1⁄4 Car Model for Suspension Trim Corrector Performances Evaluation

2016 ◽  
Vol 823 ◽  
pp. 205-210
Author(s):  
Adrian Ioan Niculescu
Keyword(s):  
Contact Force ◽  
Harmonic Functions ◽  
Degrees Of Freedom ◽  
The Body ◽  
Vertical Acceleration ◽  
Vertical Movements ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Quarter Car

The paper presents a complex quarter car model obtained with ADAMS software, View module, useful in the first stage of suspension dimensioning and optimization.The model is equipped with compression and rebound stopper buffer and suspension trim corrector.The proposed quarter car model with two degrees of freedom (wheel and body) performs all these goals allowing changing:Geometrical elementsPosition of equilibrium, depending on vehicle load;Trim correction;Elastic and dissipative characteristics of the suspension and tire;Suspension stroke;Road profile, assessed either by simple or summation of harmonic functions or reproducing real roadsBuffers (for stroke limitation) position and characteristics;The models developed provide information on:Vertical stability assessed by vertical movements of the body and the longitudinal and transversal stability evaluated based on adherence characterized by wheel ground contact force and frequency of soil detachment wheel.Comfort assessed on the basis of body vertical acceleration and collision forces to the stroke ends.The body-road clearanceThe trim corrector efficiencyAll above performances evaluated function the road unevenness, acceleration, deceleration, turning regime.The damping characteristic is defined by damping forces at different speed for each strokes respectively one for rebound and other for compression.The contact force road-wheel is defined based tire rigidity law.The stopper buffer forces on rebound and compression are defined based each specific rigidity characteristics.The road excitation is realized with a function generator.The software allow the model evolution visualisation in real time, also generating the diagrams of displacements, forces, accelerations, speeds, for each elements or for relative evolution between diverse elements.The simulation was realized for unloaded and fully loaded car using a road generated by a sum of harmonic functions presented in equation (8).The excitation covers the specific frequencies area, being under the body frequencies up to the wheel proper frequencies.The realized ¼ car model, have reached the goal to evaluate the suspension trim correction advantages.The simulations confirm the trim corrector increases the suspension performances, thus for the analyzed case the trim corrector increase simultaneous:Body-ground clearance (evaluated by body higher increasing) between 18.5÷55.1 %Body stability (evaluated by maximal body displacement) between 9.8÷11.4 %Body comfort (evaluated by maximal body acceleration) between 3.4÷35.5 %Adherence (evaluated by maximal and RMS wheel-groundcontact force variation) between 7.0÷12.1 %Body and axles protection (evaluated by buffer strike force) between 10.8÷38.2 %

Optimal Design of Active Suspensions Using Damping Control

1997 ◽  
Vol 119 (4) ◽  
pp. 609-611 ◽  
Author(s):  
Junghsen Lieh
Keyword(s):  
Feedback Signal ◽  
Active Suspensions ◽  
Active Systems ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Damping Control ◽  
Road Roughness ◽  
Optimal Damping ◽  
Second Order Equations

This paper studies the effect of optimal damping control suspensions on vehicle ride performance. The gain matrix is developed from second-order equations with the road roughness represented by a stochastic process. With only velocities as the feedback signal, the number of unknowns and measurements is reduced leading to more efficiency in data processing. The control is implemented on a quarter-car model which includes the tire damping effect. The spectral density is compared with those for passive and fully active systems.

scholarly journals Chaotic vibration of a quarter-car model excited by the road surface profile

2008 ◽  
Vol 13 (7) ◽  
pp. 1373-1383 ◽  
Author(s):  
Grzegorz Litak ◽  
Marek Borowiec ◽  
Michael I. Friswell ◽  
Kazimierz Szabelski
Keyword(s):  
Surface Profile ◽  
Road Surface ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Chaotic Vibration ◽  
Quarter Car

scholarly journals Mixed Skyhook and FxLMS Control of a Half-Car Model with Magnetorheological Dampers

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Piotr Krauze ◽  
Jerzy Kasprzyk
Keyword(s):  
Control Strategies ◽  
Mr Damper ◽  
Front Axle ◽  
Vehicle Body ◽  
Magnetorheological Dampers ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Road Roughness ◽  
Suspension Model

The problem of vibration attenuation in a semiactive vehicle suspension is considered. The proposed solution is based on usage of the information about the road roughness coming from the sensor installed on the front axle of the vehicle. It does not need any preview sensor to measure the road roughness as other preview control strategies do. Here, the well-known Skyhook algorithm is used for control of the front magnetorheological (MR) damper. This algorithm is tuned to a quarter-car model of the front part of the vehicle. The rear MR damper is controlled by the FxLMS (Filtered-x LMS) taking advantage of the information about the motion of the front vehicle axle. The goal of this algorithm is to minimize pitch of the vehicle body. The strategy is applied for a four-degree-of-freedom (4-DOF) vehicle model equipped with magnetorheological dampers which were described using the Bouc-Wen model. The suspension model was subjected to the road-induced excitation in the form of a series of bumps within the frequency range 1.0–10 Hz. Different solutions are compared based on the transmissibility function and simulation results show the usefulness of the proposed solution.

scholarly journals The vibrations induced by surface irregularities in road pavements – a Matlab® approach

2013 ◽  
Vol 6 (3) ◽  
pp. 267-275 ◽  
Author(s):  
M. Agostinacchio ◽  
D. Ciampa ◽  
S. Olita
Keyword(s):  
Dynamic Load ◽  
Variable Speed ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Road Pavement ◽  
Vehicle Mass ◽  
Road Roughness ◽  
Surface Irregularities ◽  
Iso 8608

Abstract Purpose The paper tackles the theme of evaluating dynamic load increases that the vehicle transfers to the road pavement, due to the generation of vibration produced by surface irregularities. Method The study starts from the generation, according to the ISO 8608 Standard, of different road roughness profiles characterized by different damage levels. In particular, the first four classes provided by ISO 8608 were considered. Subsequently, the force exchanged between the pavement and three typologies of vehicles (car, bus and truck) has been assessed by implementing, in Matlab®, the QCM (Quarter Car Model) characterized by a quarter vehicle mass and variable speed from 20 to 100 km/h. The analysis allows determining the amount of dynamic overload that causes the vibrational stress. Results/Conclusions The paper shows how this dynamic overload may be predetermined as a function of the pavements surface degradation. This is a useful reference for the purposes of designing and maintaining road pavements.

Optimization of Asymmetric Damper Parameters of an Automotive Suspension for Minimal Camber Angle Variations

2010 ◽  
Author(s):  
Krishna Prasad Balike ◽  
Subhash Rakheja ◽  
Ion Stiharu
Keyword(s):  
Ride Comfort ◽  
Dynamic Responses ◽  
Simulation Studies ◽  
Angle Variation ◽  
Quarter Car Model ◽  
Car Model ◽  
Camber Angle ◽  
Nonlinear Relation ◽  
Automotive Suspension ◽  
Design Guidance

Asymmetric dampers invariably employed in automotive suspensions are known to cause ‘damper jacking’. The influence of the damper jacking on the suspension kinematic responses, particularly variations in the camber angle, are generally ignored while synthesizing a damper. This study presents influences of damper asymmetry on the camber angle variations of a double wishbone type of suspension together with the dynamic responses under measured urban road inputs. Simulation studies employing a kineto-dynamic quarter-car model comprising a bilinear damper revealed increase in the camber angle variations with an increase in the damper asymmetry, while this increment showed nonlinear relation with the suspension deflection. This study further investigates synthesis of an optimal two-stage asymmetric damper to yield a compromise between the conflicting performance measures. A composite performance index comprising the ride comfort and road holding measures with limit constraint on camber angle variation is formulated to seek optimal damper parameters. The results are presented so as to yield design guidance for synthesis of asymmetric dampers.

Effects of Pavement Roughness on Rigid Pavement Stress

2011 ◽  
Vol 27 (1) ◽  
pp. 1-8 ◽  
Author(s):  
C.-M. Kuo ◽  
C.-R. Fu ◽  
K.-Y. Chen
Keyword(s):  
Coupled System ◽  
Vehicle Speed ◽  
Rigid Pavement ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Pavement Roughness ◽  
Stress Fluctuation ◽  
Roughness Index ◽  
Extreme Responses

ABSTRACTPavement roughness causes pavement stress fluctuation along the road. However, the dynamic effects were not taken into account in most pavement design and studies. To investigate the influences of roadway roughness on pavement stresses, this study developed a coupled system consisting of a quarter-car model and an equivalent lump pavement model. The coupled system also incorporated measured road profiles. By means of transfer function in frequency domain, the deflections and stresses of pavements were computed in seconds. The results were validated with Westergaard's solutions satisfactorily. It was found that the critical roughness, which might cause extreme responses, is related to the vehicle speed and suspension of vehicles. The maximum tension at the bottom of pavements also depends on the size of bump. In addition, the study demonstrates the correlation between roughness index, IRI, and ISO roughness classifications. It was also found that disturbance due to model boundary affects simulation results significantly.

Nonlinear vibration of a quarter-car model excited by the road surface profile

PAMM ◽  
2008 ◽  
Vol 8 (1) ◽  
pp. 10893-10894 ◽  
Author(s):  
Grzegorz Litak ◽  
Marek Borowiec
Keyword(s):  
Nonlinear Vibration ◽  
Surface Profile ◽  
Road Surface ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Quarter Car

scholarly journals Dynamic Vehicle and Rigid Road Interaction Analysis and Vibration Control of the Quarter Car Model Using Adaptive Neuro Fuzzy Algorithm

2021 ◽  
Vol 4 (1) ◽  
pp. 119-128
Author(s):  
Mehmet Akif Koç
Keyword(s):  
Mathematical Formulation ◽  
Suspension System ◽  
Vehicle Body ◽  
Training Process ◽  
Fuzzy Algorithm ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Road Profile ◽  
Neuro Fuzzy

In this study 3-DOF quarter car model with the three bumps on the rigid road, the assumption has been modeled with the non-random irregularity. To reduce the excessive vibrations occurred on the vehicle body, an active suspension system with the linear actuator has been considered. Moreover, to control this actuator, an adaptive neuro-fuzzy algorithm is designed. The training and testing data of the ANFIS has been obtained from Proportional Integral Derivative (PID) control algorithm. After that the successful training process, a testing procedure has been applied to ANFIS for the measure of the adaptive neuro-fuzzy system with data that are not considered in the training process. Then, the performance of the ANFIS is compared by the PID algorithm and passive suspension system in terms of vehicle body vertical acceleration, vehicle body vertical displacement, and control force. The road model used in the study has been modeled according to non-random road profile mathematical formulation considering periodical and discrete road profile cases. In this formulation, one can easily determine the height, width, and number of the road defect with the series mathematical formulation. Consequently, with the results obtained from the presented study, it is proven that ANFIS is a very effective controlling algorithm to suppress vibration occurred on the vehicle body due to vehicle road interaction. Furthermore, the performance of the ANFIS has been tested with different parameters, for example, different number membership functions (MF), which used the fuzzification of the input parameters.

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